We show that correlated dynamics and long time memory persist in self-organized criticality (SOC) systems even when
forced away from the defined critical point that exists at vanishing drive strength. These temporal correlations are found
for all levels of external forcing as long as the system is not overdriven. They arise from the same physical mechanism that
produces the temporal correlations found at the vanishing drive limit, namely the memory of past events stored in the
system profile. The existence of these correlations contradicts the notion that a SOC time series is simply a random
superposition of events with sizes distributed as a power law, as has been suggested by previous studies.